List of top Mathematics Questions

In a class of 60 students, mathematics examination was conducted. All the students obtained 20 marks each. What would be the mean and standard deviation of marks in mathematics?
If \( \vec{A} = 2\hat{i} + 3\hat{j} \) and \( \vec{B} = 4\hat{i} - \hat{j} \), then the dot product \( \vec{A} \cdot \vec{B} \) is:
Find the area of a triangle with base 12 cm and height 5 cm.
Solve for $ x $ in the equation $ \frac{1}{x+3} + \frac{1}{x+5} = \frac{1}{6} $.
If $ \tan \theta = \frac{3}{4} $, find the value of $ \sin \theta $.
Find the value of $ x $ that satisfies the equation $ 2x + 3 = 11 $.
Find the roots of the quadratic equation $ x^2 - 5x + 6 = 0 $.
Evaluate the expression: \[ f\left(f(f(x))\right) + \left(f(f(x))\right)^2 \quad \text{if} \quad x = 1 \]
Evaluate the determinant of the matrix: \[ \left| \begin{array}{cc} 1 & \tan x
-\tan x & 1 \end{array} \right| \]
Evaluate the integral: \( \int \sin^5 x \, dx \)
Find the value of \( \tan 45^\circ \).
Find the value of \( \frac{d}{dx} (3x^2 + 4x + 5) \).
If the sum of the first \( n \) terms of an arithmetic progression (AP) is given by \( S_n = 3n^2 + 2n \), find the 4th term of the AP.
Find the value of \( \log_2 32 \).
Find the area of a circle whose radius is 7 cm.
If \( \sin \theta = \frac{3}{5} \), find the value of \( \cos \theta \).
The sum of the ages of a father and his son is 60 years. The father is three times as old as the son. What is the son's age?
Find the value of \( \sin 30^\circ + \cos 60^\circ \).
The area of a triangle with base 12 cm and height 5 cm is?
If \( y = x^x + x^x \), then find \( \frac{dy}{dx} \):
The number of four digit even numbers that can be formed using the digits 0, 1, 2 and 3 without repetition is:
If ∫ (2x + 3)/((x - 1)(x^2 + 1)) dx = log_x {(x - 1)^(5/2)(x^2 + 1)^a} - (1/2) tan^(-1)x + C, then the value of a is:
Find the value of the integral: ∫ (2x + 3)/((xy)(x^2 + 1)) dx
If the system of equations \[ x + 2y - 3z = 2 \] \[ 2x + \lambda y + 5z = 5 \] \[ 4x + 3y + \mu z = 33 \] has infinite solutions, then \( \lambda + \mu \) is equal to
If the sum, \( \sum_{r=1}^9 \frac{r+3}{2r} \cdot \binom{9}{r} \) is equal to \( \alpha \cdot \left( \frac{3}{2} \right)^9 - \beta \), then the value of \( (\alpha + \beta)^2 \) is equal to: